Integral bases for the universal enveloping algebras of map algebras

Given a finite-dimensional, simple Lie algebra g over C and A, a commutative, associative algebra with unity over C, we exhibit an integral form for the universal enveloping algebra of the map algebra, U(g circle times A), and an explicit Z-basis for this integral form. We also produce explicit commutation formulas in the universal enveloping algebra of sl(2) circle times A that allow us to write certain elements in Poincare-Birkhoff-Witt order. (C) 2012 Elsevier Inc. All rights reserved.